Restoring structural controllability of interdependent multi-layered heterogenous cyber-physical-social networks via optimal network reconfiguration

This paper addresses the critical challenge of restoring structural controllability in cyber-physical-social systems (CPSS) compromised by cyber-attacks. Unlike existing studies that focus on homogenous networks or neglect the role of interlayer couplings and intralayer topologies, this work introduces a novel approach to enhance cyber resilience in interdependent multi-layered heterogenous CPSS. We establish new necessary and sufficient conditions for achieving post-attack structural controllability and propose an optimal network reconfiguration algorithm that restores controllability with minimal intervention. This novel algorithm identifies the minimum set of edges required to reconfigure this network, ensuring structural controllability in a polynomial time. Our approach is validated through simulations on various CPSS, including IEEE 14-bus and IEEE 118-bus power networks, as well as scale-free, clustered scale-free, small-world, and random networks subjected to various attack strategies. Additionally, the approach is applied to real-world large-scale datasets, demonstrating its scalability and practical applicability. The results reveal that, among intralayer topologies, scale-free networks are highly vulnerable to structural uncontrollability. Furthermore, sparse interlayer coupling significantly reduces the resilience of the CPSS compared to mesh and peer-to-peer (P2P) coupling configurations. Notably, targeted attacks based on betweenness require about 53 % more edge additions to restore controllability compared to random attacks.